Simulations of an impulsive model for the growth of fruit trees

Mediterranean agricultural systems have been severely affected because of the decrease in rainfall and more frequent and severe droughts due to the global warming phenomenon. The current and future scenario of water deficit could have a negative effect on the growth and development rates of the fruit trees, reflected in the drop of production. To help to face this problem, this work presents a mathematical simulation model of fruit growth with two-time scales: a continuous scale that governs the dynamics of fruit growth and a discrete scale representing the period of time in which the system is intervened with irrigation supply. The results obtained in the simulations allow us to describe and understand the physical phenomena involved in the growth dynamics of fruit trees. In addition, show the importance of the water resource for the growth and development of fruit trees; therefore, a scenario of water deficit would compromise the production and existence of fruit trees.

Periodic Solution of A Delayed Intraguild Predation Impulsive System with Strong Allee Effect

With periodic coefficients and strong Allee effects, we establish a delayed intraguild predation impulsive model. We obtain a set of sufficient conditions for the existence of positive periodic solution of the model using Mawhin’s continuation theorem and analysis techniques. Finally, we identify the effectiveness of the theoretical results through some numerical simulations.

Impulsive Fire Disturbance in a Savanna Model: Tree–Grass Coexistence States, Multiple Stable System States, and Resilience

Savanna ecosystems are shaped by the frequency and intensity of regular fires. We model savannas via an ordinary differential equation (ODE) encoding a one-sided inhibitory Lotka–Volterra interaction between trees and grass. By applying fire as a discrete disturbance, we create an impulsive dynamical system that allows us to identify the impact of variation in fire frequency and intensity. The model exhibits three different bistability regimes: between savanna and grassland; two savanna states; and savanna and woodland. The impulsive model reveals rich bifurcation structures in response to changes in fire intensity and frequency—structures that are largely invisible to analogous ODE models with continuous fire. In addition, by using the amount of grass as an example of a socially valued function of the system state, we examine the resilience of the social value to different disturbance regimes. We find that large transitions (“tipping”) in the valued quantity can be triggered by small changes in disturbance regime.

Dynamic Analysis of a Plankton-Herbivore State-Dependent Impulsive Model With Action Threshold Depending On The Density and Its Changing Rate

A plankton-herbivore state-dependent impulsive model with nonlinear impulsive functions and action threshold including population density and rate of change is proposed. Since the use of action threshold makes the model have complex phase set and pulse set, we adopt the Poincaré map as a tool to study its complex dynamics. The Poincaré map is defined on the phase set and its properties in different situations are analyzed. Furthermore, the periodic solution of model are discussed, including the existence and stability conditions of the order-1 periodic solution and the existence of the order-k (k ≥ 2) periodic solutions. Compared with the fixed threshold in the existing literature, our results show that the use of action threshold is more practical, which is conducive to the sustainable development of population and makes people obtain more economic benefits. The analysis method used in this paper can study the complex dynamics of the model more comprehensively and deeply.

Putting the pieces together: Self-control as a complex interaction of psychological processes

Ainslie's account of willpower addresses many important mechanisms (e.g., habit, visceral activation, and implementation intention). We argue that a model of willpower should be grounded in general psychological principles and with a primary focus on their interplay. We discuss the reflective-impulsive model that covers willpower and impulsiveness as special constellations of processes that govern various forms of cognition and behavior.